The goal of this article is to present an introduction to loop quantum gravity â€”a background independent, non-perturbative approach to the problem of unification of general relativity and quantumâ€¦ (More)

A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulatedâ€¦ (More)

In a quantum mechanical treatment of gauge theories (including general relativity), one is led to consider a certain completion, A/G, of the space A/G of gauge equivalent connections. This spaceâ€¦ (More)

Holonomy algebras arise naturally in the classical description of Yang-Mills fields and gravity, and it has been suggested, at a heuristic level, that they may also play an important role in aâ€¦ (More)

Abhay Ashtekar, Jerzy Lewandowski 1 Center for Gravitational Physics and Geometry Department of Physics, Penn State, University Park, PA 16802-6300, USA 2 Instytut Fizyki Teoretycznej, Uniwersytetâ€¦ (More)

Asymptotically anti-de Sitter space-times are considered in a general dimension d â‰¥ 4. As one might expect, the boundary conditions at infinity ensure that the asymptotic symmetry group is theâ€¦ (More)

Using the classical Hamiltonian framework of [1] as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting non-rotatingâ€¦ (More)

An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detailâ€¦ (More)

A `black hole sector' of non-perturbative canonical quantum gravity is introduced. The quantum black hole degrees of freedom are shown to be described by a Chern-Simons eld theory on the horizon. Itâ€¦ (More)

A framework was recently introduced to generalize black hole mechanics by replacing stationary event horizons with isolated horizons. That framework is significantly extended. The extension isâ€¦ (More)